Abstract

(Baudouin and Puel 2002 Inverse Problems 18 1537-54), investigated some inverse problems for the evolution Schrödinger equation by means of Carleman inequalities proved under a strict pseudoconvexity condition. We show here that new Carleman inequalities for the Schrödinger equation may be derived under a relaxed pseudoconvexity condition, which allows us to use degenerate weights with a spatial dependence of the type ψ(x) = x e, where e is some fixed direction in . As a result, less restrictive boundary or internal observations are allowed to obtain the stability for the inverse problem consisting in retrieving a stationary potential in the Schrödinger equation from a single boundary or internal measurement. © 2008 IOP Publishing Ltd.